For the number $65=5.13=2^6+1$

Problem's Description

Problem. Are there infinitely many natural numbers $n$, for which \[ 2^n+1=p.q, \] where $p$ and $q$ are different prime numbers ?

Suggestion. Numerical experiments show that there are infinitely many numbers $n$ with the above property. Are there an asymptotic for these $n$ ?

1. Book 250 problems on elementary number theory

   • W. Sierpinski

   year of publication: 1968